Does this expression make sense.

[Klaus_Hoffmann]

i don't know where i saw the question is does this expression (Cesaro sum ??) make sense for big lambda and positive delta

$$\sum_{n \le \lambda } (1- \frac{n}{\lambda})^{\delta} \mu (n)=S( \lambda , \delta)$$

for finite lambda the S is finite the question is what would happen as lambda goes to infinity ?, does the sum converge in the sense that for lambda big.

$$S \sim A+ O( \lambda ^{-b}$$ (b a positive real number)

and the same for

$$\sum_{n \le \lambda } (1- \frac{n}{\lambda})^{\delta} \Lambda (n)=S( \lambda , \delta)$$

 

[matt grime]

What have you tried to prove, or disprove, and how have you attempted to do it?